A class function on the Torelli group
type: Item
instance of: scholarly article
title: A class function on the Torelli group
zbMATH Open document ID: 1072.57014
author: Masaaki Suzuki
published in: Kodai Mathematical Journal
publication date: 2004-08-16T00:00:00Z
review text: Let \(\Sigma_{g,1}\) be a compact orientable surface of genus \(g\) with one boundary component. The Torelli group of \(\Sigma_{g,1}\) is defined to be the subgroup of the mapping class group of \(\Sigma_{g,1}\) acting trivially on the first integral homology \(H=H_1(\Sigma_{g,1};{\mathbb{Z}})\). The Magnus representation of \(r_1\) is a map from the Torelli group to the group \(GL(2g,{\mathbb{Z}}[H])\) defined by using the Fox derivative on the integral group ring of the fundamental group of \(\Sigma_{g,1}\), a free group of rank \(2g\). The paper under review investigates some properties of the characteristic polynomials of the images of elements of the Torelli group under the map \(r_1\).
reviewed by: Mustafa Korkmaz
Mathematics Subject Classification ID: 57M99
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 2091928
zbMATH Keywords: Torelli group
zbMATH Keywords: Magnus representation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1073670611
OpenAlex ID: W2093213440
DOI: 10.2996/KMJ/1073670611
description: scientific article; zbMATH DE number 2091928